VOLUME 70, NUMBER 4 PH YSICAL REVIEW LETTERS 25 JANUARY 1993

Atoms in Strong Optical Fields: Evolution from Multiphoton to Tunnel Ionization

Eric Mevel, Pierre Breger, Rusty Trainham, Guillaume Petite, and Pierre AgostiniService de Recherches sur les Surfaces et I'Irradiation de la Matiere, Centre d'Etude de Sac!ay,

9l l 9I Gif Sur -Yvet-te, France

Arnold Migus, Jean-Paul Chambaret, and Andre AntonettiI aboratoire O'Optique Appliquee, Ecole Nationale Superieure de Techniques Avancees, Ecole Polytechnique,

91120 Palaiseau, France(Received 24 August 1992)

Electron energy spectra from ionization of the noble gases by 617-nm, 100-fs intense laser pulses showthat the periodical double structure of narrow Stark-induced resonances and above-threshold ionizationdisappears gradually from xenon to helium. This implies that shifts and widths become of the order ofthe atomic-orbital frequencies, as expected at the onset of the tunneling regime.

PACS numbers: 32.80.Fb, 32.80.Rm, 32.80.&r

The behavior of atoms under strong irradiation hasbeen a subject of constant interest ever since powerfullaser sources became available. Although it is now rela-tively easy to produce extremely intense electromagneticfields from compact, laboratory-sized laser systems, it isnot possible to submit a given atom to an arbitrarily highintensity because it will be ionized before sensing thepeak of the pulse. The maximum practical intensity, thesaturation intensity, as defined by Lambropoulos [1], thatcan be applied to a neutral atom is determined by its ion-ization probability and the pulse characteristics. Theupper limit for the saturation is reached by using state-of-the-art intense 70-fs pulses. The highest saturation in-

tensities are obtained, under given laser conditions, withatoms having the highest ionization potential (e.g. , heli-um). However, the ionization rate is too small to allow astudy of the interaction at low intensities. A qualitativeidea of the atomic behavior over a large range of intensi-ties can nevertheless be obtained by studying similaratoms with increasing ionization potentials. The raregases are well suited for this purpose and convenientlyprovide targets which span a factor of 2 in ionization po-tential and more than 10 in saturation intensities.

Ionization is one of the possible outcomes of the light-atom interaction. In the regime of strong fields, multi-photon ionization (MPI) and tunnel ionization (TI) arethe two limiting cases of the ionization process [2]. Theratio y of the tunneling time (i.e., the width of the barrierdivided by the electron velocity) to the optical period is

known as the adiabaticity or Keldysh parameter and is

generally used to separate the two regimes,

) =(IP/2U, ) '",where IP is the atom ionization potential and Uz the pon-deromotive potential of the laser,

In the low frequency limit (y « I ), TI is a gooddescription of the transition dynamics. This is typical ofrare gases ionized by a CO2 laser, in which case the elec-tron tunnels out in a time less than half the field periodwhile its energy and momentum are subsequently deter-

mined by the Lorentz force [3]. In the other limit(y»1), the multiphoton character is evident in the pho-toelectron spectra as a structure repeated with the photonenergy period [above-threshold ionization (ATI)] andwhose rate scales as I, where I is the intensity and 1V thenumber of absorbed photons. This is typically the casefor visible or uv excitation of an alkali atom. The ioniza-tion of rare gases by visible or near-infrared light spans arange of y's large enough to encompass both limits. Ac-cording to the definition above, y seems to be an increas-ing function of IP. However, y is an intensity-dependentparameter through U~. Therefore, the effective value of ydepends on the intensity at which the ionization is actual-ly observed. It is qualitatively obvious that this intensityis an increasing function of the ionization potential. Aquantitative estimate (known to be in good agreementwith the experiment [4]) can be obtained by taking thethreshold intensity for a (dc) field ionization,

lych =IP /16Z (2)

in the definition of U„in (1). The result of this substitu-tion is that y actually scales as IP and therefore de-creases from xenon to helium. Furthermore, due to satu-ration, the effective y in an experiment depends also onthe pulse rise time. For short pulses, good agreementwith the tunnel ionization rate [S] was found [6,7].

To study ionization, one possible option is to measurethe power law of the total yield as a function of the in-cident intensity. However, it is also well known that suchmeasurements are difficult and may lead to inconclusiveresults. The energy spectra of the photoelectrons result-ing from the interaction between a laser pulse and anatom are known to carry somewhat more informationthan the ions. Many features that had remained hiddenin total ion yield measurements have been uncovered byelectron spectroscopy: the nonperturbative character ofATI, Stark-induced resonances (Freeman et al. [8]), etc.

These were the two basic motivations of the currentwork, in which we try to reconstruct a typical atomicresponse to strong fields over a large intensity range from

406 1993 The American Physical Society

VOLUME 70, NUMBER 4 PH YSICAL REVIEW LETTERS 25 JANUARY 1993

I I I I I I I I I1

I I I I I I I I I I I I I I I I I I I

4f 4f

O

7p

7p

m

OV

0 1 2 3 4 5 6E (eV)

FIG. 1. Electron energy spectrum from xenon at 6.2X10'W cm . Note that the resonances are reproduced with thephoton energy perrod (2 eV).

10 20 30E (eV)

~ ~ I

40 50

FIG. 2. Electron energy spectrum from neon at 6 x 10'Wcm . ATI is still seen superimposed on a large background.

the spectra obtained with the difTerent rare gases.Briefly, a colliding pulse mode-locked oscillator is am-plified in five Bethune dye cells and produces a maximumoutput energy of 2 mJ per pulse at a repetition rate of 20Hz and a pulse duration as short as 75 fs at 617 nm. Thelinearly polarized beam is focused inside the interactionchamber by an achromatic doublet with an f number of3, giving rise to intensities in excess of 5x 10' WcmThe electron spectrometer is a 1-m-long time-of-flighttube with a parabolic mirror electrostatic optic [9] whichhas a collection eSciency larger than 50% and a resolu-tion of 50 meV at 1 eV. Electrons are detected by a dual50-mm-diam multichannel plate detector with single-electron detection capability and signal processing is car-ried out by a digital oscilloscope with a 400-MHz sam-

pling rate. The background pressure in the spectrometeris 2x10 torr. The target gas is leaked in the chamberat pressures varying from 10 to 10 torr which en-sures a constant signal of a few counts per laser shot.The shot-to-shot pulse energy is monitored by a photo-diode and this signal is used to store the electron data in

up to ten diAerent bins. Thus, it is possible to reduce theintensity fluctuations for a given bin to a few percent.The various bins are filled by varying the intensity with ahalf-wave-plate-polarizer combination and the naturalshot-to-shot fluctuations.

By setting a negative voltage on the flight tube while

keeping the paraboloids at ground, a field is created in-side the parabola and ions can be collected and mass ana-lyzed. The typical resolution is about 100 at M=132(the xenon isotopes are barely resolved). This has beenused to analyze the background ionization, to ensure thatonly one charge state is obtained (negligible multiple ion-ization), and to measure the total yield.

The evolution of the photoelectron energy spectra fromxenon to helium is summarized in Figs. 1 to 3. The spec-tra of the lowest IP gases, xenon (IP =12.13 eV) (seeFig. 1), krypton (IP =13.99 eV), and argon (IP =15.76eV), show a series of Stark-induced resonances which arereproduced in the difterent ATI orders. The resonancesobviously dominate the transitions and, for xenon and ar-

1 10

B~ W

8 10

6 10

4 10

2 10

P 1PO E I ~ ~ ~

0 50 150E (eV)

FIG. 3. Electron energy spectrum from helium at 1.5 X 10'W cm . ATI and resonances have disappeared similar to thecase of tunneling.

gon, the spectra are relatively robust against intensitychanges. As the peak intensity is increased beyond theappearance intensity, more resonances appear towardslow energies but the spectra maintain their general struc-ture. Therefore, from xenon to argon the ionization pro-cess keeps a clear multiphoton character in the sense thatboth the atomic structure and the photon energy play themajor role and are clearly apparent on the spectra.

In xenon, the now well-known six-photon resonances ofthe nf states are observed (n =4, 8). The appearance in-

tensity is about 0.4 x 10' W cm corresponding to theSf resonance. A small contribution from the p states is

also detected. Another resonance appears at 3.9&10'Wcm (Fig. 1) due to the 7p state. As the peak inten-

sity is increased beyond 6X10' Wcm, the spectrashow essentially no change in structure for a given ATIorder but the relative amplitudes of the diAerent ordersare changing. The dynamics of the ATI structure in thepresence of resonances will be analyzed elsewhere to keepthis paper focused. The resonant processes are clearlydominant over the nonresonant ones, as seen from the low

background between the resonant structure.In krypton, the appearance intensity is 1.5 x 10'

Wcm and, again, the resonances dominate. However,the intensity behavior of the spectra is in strong contrast

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VOLUME 70, NUMBER 4 PH YSICAL REVIEW LETTERS 25 JANUARY 1993

with the previous ones: The resonances merge into a con-tinuum up to 9x10' Wcm and a strong resonance,identified as the 4f state, eventually emerges for intensi-ties beyond this value. This corresponds to an exception-ally large Stark shift, as discussed in detail by Mevel etal. [10] due to a combination of favorable factors (largestatic detuning of 2.9 eV) and high saturation intensity.In spite of this unusual behavior, the ionization processremains undoubtedly multiphoton.

In argon, the spectra again show outstanding reso-nances and behave similarly as the intensity is increased.Quantitatively, the intensity necessary to obtain spectra is

1 x 10' W cm, but the appearance intensity is 2.5x10' Wcm . The saturation intensity is about 2x10' Wcm

In contrast, the two lightest rare gases pr=sent spectrathat differ drastically from the previous ones. Let us con-sider neon first. Its IP is significantly higher (21.56 eV)and so is the appearance intensity (1.6x10' Wcm ).The electron energy spectrum (Fig. 2) is observed up toan energy of 50 eV and presents a series of broad peaks~hose separation is the photon energy. Some substruc-tures still seem to be present in the spectra but they havenot been identified. In conclusion, the multiphoton char-acter is still obvious.

Finally, in helium, the appearance intensity is about 40times larger than for xenon (2.5&&10' Wcm ). Asshown in Fig. 3 the electron spectrum, which extends to90 eV, does not show structure above 30 eV. The chaoticspiking seen below is not reproducible, di%cult to smoothout, and showing no relation with the photon energy.Checks have been carried out to ensure that structuresare not washed out by space charge broadening. Themost straightforward one is to leak in xenon gas at thesame time as helium and record the spectrum at the heli-um intensity. The well-identified xenon structures re-mained quite resolved, thus demonstrating that their ab-sence in the helium spectrum is not connected with an in-strumental artifact. The contribution from impurities in

the helium bottle (mostly H+, H2+, H20+) was alsochecked by recording mass spectra. They do not contrib-ute more than a few percent to the total ion signal. Fi-nally, broadening by ponderomotive acceleration is ruledout since the pulse turns off much faster than the time forelectrons to escape the beam focus. For instance, at1.5x10' Wcm, the drift velocity is 4.3x10' msand the electron exit time for a 10-pm focus is 1.15 ps.

This type of spectrum is strongly reminiscent of typicalspectra in the long wavelength limit [3], that is, of field ortunnel ionization. This view is also supported by themeasured ion yield which scales as I, in good agreementwith the prediction for tunneling [5]. In the low frequen-cy limit, ionization is a quasi-instantaneous process leav-ing the free electron with a zero velocity. The electronfinal kinetic energy is determined by the classical motionin the electromagnetic field and the time at which the

10

C4

o . Xe Kr

'oAr

Ne

010 15 20 25

Ionization Potential (eV)30

FIG. 4. y values corresponding to appearance (0) and satu-ration (0) intensities. The solid lines indicate the range ofvalues accessible to experiment for each gas.

electron is created [3]. In the case of linear polarization,this time is a fraction of the optical period around thecrests and the troughs of the field oscillations. However,the disappearance of all structures in the spectrum is not,per se, a proof of the tunneling regime. Actually, a Flo-quet calculation in the case of hydrogen [11] shows thatresonant structures may still be visible as the tunnelingregime is approached. However, at intensities above thecritical intensity (at which the saddle-point potential be-comes equal to the electron binding energy), the ioniza-tion occurs in times of the order of 2x/cu,. t, where ru, , isthe atomic-orbital frequency. The Floquet calculationbecomes inadequate then but still gives an indication ofthe widths. As they are much larger than the photon en-

ergy, it implies that all structures are washed out [11].One question is whether or not the evolution of the

spectra correlates to the variation of the adiabaticity pa-rameter. Using the experimental intensities, one gets the

y values shown in Fig. 4. The upper and lower valuescorrespond to the experimental appearance and satura-tion intensities, respectively. It is clear that there is somecorrelation since values for xenon to krypton are aboveunity, while for neon and helium they reach values below1 where the tunneling regime begins. However, the yvalues can be only indicative since they remain close to 1

contrary to the case of CO2 laser experiments [3]. Onthe other hand, the electron spectra are significantlydifferent.

In summary, this experimental study of rare gases ion-ization by intense 100-fs, 617-nm laser pulses by electronspectrometry shows the following trend: At the lowest in-

tensity, the ionization process is unambiguously of multi-photon character and the Stark-induced resonances aredominant. States with Stark shifts as high as 2.9 eV areidentified and the corresponding resonances are still out-standing. At an intensity about 10 times larger, the reso-nances are lost but the ATI structure is still apparent.Eventually, even this structure is lost as expected when

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VOLUME 70, NUMBER 4 PHYSICAL REVIEW LETTERS 25 JANUARY 1993

the shifts and widths become comparable to the atomic-orbital frequencies and at the onset of the tunneling re-gime, when the ionization process concentrates in times ofthe order of the optical period. Both the spectrum andthe dependence of the rate as I support the view that thetunneling regime has been reached. It is the first time, toour knowledge, that this transition has been observed atoptical frequencies. It is a significant outcome of this pa-per that the results obtained in the infrared are confirmedin an experiment where the energy resolution is signif-icantly smaller than the photon energy. This trend, fromxenon to helium, may be viewed as the typical behavior ofan atom submitted to high intensity radiation, if it couldbe recorded without the saturation intensity limitation.

This work was performed at the Laboratoire d'OptiqueAppliquee (LOA) and supported by the EuropeanEconomic Community under Contract No. SC1-0103C.LOA is Unite de Recherche Associee au CNRS 1406.We would like to thank L. F. DiMauro for his criticalreading of this manuscript and very helpful discussions.

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